The study of the interaction of intense optical pulses with materials is as old as the subject of nonlinear optics itself. Experiments in the sixties established that a host of complex physical processes could act in concert as local field intensities approached the material breakdown threshold. In general, ionization of the material, electrostriction, stimulated scattering ( Raman and Brillouin 3-wave processes), thermal breakdown, and other phenomena occurred simultaneously in the breakdown region. The consequences of these interactions were generally so catastrophic that little progress could be made in establishing a quantitative understanding of the role of the separate physical processes involved[1]. Recent progress in producing ultrashort optical pulses in the femtosecond to picosecond regime has opened up the possibility of isolating these complex material interactions in bulk materials. Dimensionality of the material plays a significant role in influencing the nature of optical pulse propagation in different materials.
In transparent dielectrics, propagation in 1D (optical fibers) is best understood and has promoted many novel all-optical technology applications. Soliton telecommunications, fiber amplifiers and lasers, optical polarization switching etc have provided an excellent paradigm for the exploration of nonlinear interaction processes. The mathematical description here is simplest, affording scalar nonlinear pde (nonlinear Schrodinger (NLS) or complex Ginzburg-Landau (CGL)) or simple vector (coupled NLS/CGL) descriptions. Optical fibers behave essentially as analog computers whereby the robustness of various mathematical models can be explored in a systematic fashion. Both bright and dark solitons have been observed experimentally[2]. Optical pulse propagation in planar optical waveguides (2D) is less well understood but affords a much richer nonlinear phenomenology. Here one must distinguish between transverse electric (TE) and transverse magnetic (TM) propagating modes. Critical collapse (self- focusing ) can become a major player and novel optical pulse compression schemes based on anomolous dispersion have recently been proposed. Optical pulse propagation in bulk (3D) transparent media is least understood quantitatively but offers the greater variety of complex material interactions.
The nature of the nonlinear optical response to an incident light field can also be profoundly influenced by dimensionality of the material. In semiconductors, for example, as one or more physical dimensions of the material approaches the Bohr radius ( of the order of tens of Angstroms), quantization phenomena begin to play an important role. A more detailed discussion of this topic is provided in the article in these proceedings by Andreas Knorr and Stephan Koch. Propagation of femtosecond optical pulses in bulk (3D) and 2D Quantum Well (QW) semiconductor amplifiers will be discussed below in order to highlight these quantization effects and, in addition, provide an illustration of the complex microscopic many-body interactions arising between the light field and multi-component plasmas.